Electron transfer reaction in the marcus inverted region: role of high frequency vibrational modes

A theoretical study of the dynamics of photo-electron transfer reactions in the Marcus inverted regime is presented. This study is motivated partly by the recent proposal of Barbara et al. (J. Phys. Chem. 96, 3728, 1991) that a minimal model of an electron transfer reaction should consist of a polar solvent mode (X), a low frequency vibrational mode (Q) and one high frequency mode (q). Interplay between these modes may be responsible for the crossover observed in the dynamics from a solvent controlled to a vibrational controlled electron transfer. The following results have been obtained. (i) In the case of slowly relaxing solvents, the proximity of the point of excitation to an effective sink on the excited surface is critical in determining the decay of the reactant population. This is because the Franck-Condon overlap between the reactant ground and the product excited states decreases rapidly with increase in the quantum number of the product vibrational state. (ii) Non-exponential solvation dynamics has an important effect in determining the rates of electron transfer. Especially, a biphasic solvation and a large coupling between the reactant and the product states both may be needed to explain the experimental results. ©1996 American Institute of Physics

Non-Marcus energy gap dependence of electron transfer rate in contact ion pairs. Novel interplay between relaxation and reaction in solution

Electron transfer reactions between donor-acceptor pairs in solution and in organized media exhibit diverse behaviour. Recent experiments have indicated an interesting breakdown of the Marcus parabolic energy gap dependence in the normal regime for back electron transfer from contact ion pairs. A novel explanation of this breakdown has recently been proposed (M. Tachiya and S. Murata, J. Am. Chem. Sec., 116(1994) 2434) which attributes the breakdown to the interplay between the relaxation in the reactant well and the reaction. A particularly interesting aspect of the model is that it envisages the electron transfer in the normal regime to take place from a completely non-equilibrium condition. In this article a time dependent solution of the model is presented for the first time, after generalizing it to include a realistic initial population distribution. The decay of the contact ion pair population is completely non-exponential. This can be used to check the validity of the Tachiya-Murata model. The dynamics of electron transfer from the solvent separated ion pair, which seem to obey the Marcus relation, is exponential.

Quantum and non-Markovian effects in the electron transfer reaction dynamics in the Marcus inverted region

Electron transfer reactions in large molecules may often be coupled to both the polar solvent modes and the intramolecular vibrational modes of the molecule. This can give rise to a complex dynamics which may in some systems, like betaine, be controlled more by vibrational rather than by solvent effects. Additionally, a significant contribution from an ultrafast relaxation component in the solvation dynamics may enhance the complexity. To explain the wide range of behavior that has been observed experimentally, Barbara et al. recently proposed that a model of an electron transfer reaction should minimally consist of a low-frequency classical solvent mode (X), a low-frequency vibrational mode (Q), and a high-frequency quantum mode (q) (J. Phys. Chem. 1991, 96, 3728). In the present work, a theoretical study of this model is described. This study generalizes earlier work by including the biphasic solvent response and the dynamics of the low-frequency vibrational mode in the presence of a delocalized, extended reaction zone. A novel Green's function technique has been developed which allowed us to study the non-Markovian dynamics on a multidimensional surface. The contributions from the high-frequency vibrational mode and the ultrafast component in the non-Markovian solvent dynamics are found to be primarily responsible for the dramatic increase in charge transfer rate over the prediction of the classical theories that neglect both these factors. These, along with a large coupling between the reactant and the product states, may combine to render the electron transfer rate both very large and constant over a wide range of solvent relaxation rates. A study on the free energy gap dependence of the electron transfer rate reveals that the rates are sensitive to changes in the quantum frequency particularly when the free energy gap is very large.

Stochastic differential games with multiple modes

We have studied two person stochastic differential games with multiple modes. For the zero-sum game we have established the existence of optimal strategies for both players. For the nonzero-sum case we have proved the existence of a Nash equilibrium.

Free Energy Gap Dependence of the Electron-Transfer Rate from the Inverted to the Normal Region

numerical study of the free energy gap (FEG) dependence of the electron-transfer rate in polar solvents is presented. This study is based on the generalized multidimensional hybrid model, which not only includes the solvent polarization and the molecular vibration modes, but also the biphasic polar response of the solvent. The free energy gap dependence is found to be sensitive to several factors, including the solvent relaxation rate, the electronic coupling between the surfaces, the frequency of the high-frequency quantum vibrational mode, and the magnitude of the solvent reorganization energy. It is shown that in some cases solvent relaxation can play an important role even in the Marcus normal regime. The minimal hybrid model involves a large number of parameters, giving rise to a diverse non-Marcus FEG behavior which is often determined collectively by these parameters. The model gives the linear free energy gap dependence of the logarithmic rate over a substantial range of FEG, spanning from the normal to the inverted regime. However, even for favorable values of the relevant parameters, a linear free energy gap dependence of the rate could be obtained only over a range of 5000-6000 cm(-1) (compared to the experimentally observed range of 10000 cm(-1) reported by Benniston et al.). The present work suggests several extensions/generalizations of the hybrid model which might be necessary to fully understand the observed free energy gap dependence.

Paracrine action of sFLT-1 secreted by stably-transfected Ehrlich ascites tumor cells and therapy using sFLT-1 inhibits ascites tumor growth in vivo

Background Vascular endothelial growth factor (VEGF) is known to play a major role in angiogenesis. A soluble form of Flt-1, a VEGF receptor, is potentially useful as an antagonist of VEGF, and accumulating evidence suggests the applicability of sFlt-1 in tumor suppression. In the present study, we have developed and tested strategies targeted specifically to VEGF for the treatment of ascites formation.Methods As an initial strategy, we produced recombinant sFLT-1 in the baculovirus expression system and used it as a trap to sequester VEGF in the murine ascites carcinoma model. The effect of the treatment on the weight of the animal, cell number, ascites volume and proliferating endothelial cells was studied. The second strategy involved, producing Ehrlich ascites tumor (EAT) cells stably transfected with vectors carrying cDNA encoding truncated form of Flt-1 and using these cells to inhibit ascites tumors in a nude mouse model. Results The sFLT-1 produced by the baculovirus system showed potent antiangiogenic activity as assessed by rat cornea and tube formation assay. sFLT-1 treatment resulted in reduced peritoneal angiogenesis with a concomitant decrease in tumor cell number, volume of ascites, amount of free VEGF and the number of invasive tumor cells as assayed by CD31 staining. EAT cells stably transfected with truncated form of Flt-1 also effectively reduced the tumor burden in nude mice transplanted with these cells, and demonstrated a reduction in ascites formation and peritoneal angiogenesis. Conclusions The inhibition of peritoneal angiogenesis and tumor growth by sequestering VEGF with either sFlt-1 gene expression by recombinant EAT cells or by direct sFLT-1 protein therapy is shown to comprise a potential therapy. Copyright (C) 2009 John Wiley & Sons, Ltd.

In vivo treatment of Heymann's Nephritis using a cytotoxic protein-toxin conjugate

In this study we investigated the possibility of treating Heymann's Nephritis (HN) by destroying antibody producing cells by targetting a toxin, gelonin - conjugated to gp330, the renal brush border antigen. HN was induced in rats by immunizing them with purified gp330. The gelonin-gp330 conjugate was administered 12 days after the antigenic challenge. Serum was screened for circulating antibodies. Proteinurea was estimated. The gp330-gelonin conjugate-treated animals had a circulating antibody titre in the serum much lower than that of diseased (untreated) animals. Proteinurea seen in diseased animals was not observed in treated animals. This work suggests the possibility of using a toxin-antigen conjugate for immunomodulating antibody mediated autoimmune renal disease.

Polarization Caging in Diffusion-Controlled Electron Transfer Reactions in Solution

In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P-(1)(X,R,t)) and the product (p((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent, As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.

Discrete-Time Controlled Markov Processes with Average Cost Criterion: A Survey

This work is a survey of the average cost control problem for discrete-time Markov processes. The authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades. The exposition ranges from finite to Borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies. The authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography. The authors have also identified several important questions that are still open to investigation.

Effects of Ultrafast Solvation on the Rate of Adiabatic Outer-Sphere Electron Transfer Reactions

Recent studies have demonstrated that solvation dynamics in many common dipolar liquids contain an initial, ultrafast Gaussian component which may contribute even more than 60% to the total solvation energy. It is also known that adiabatic electron transfer reactions often probe the high-frequency components of the relevant solvent friction (Hynes, J. T. J. Phys. Chem. 1986, 90, 3701). In this paper, we present a theoretical study of the effects of the ultrafast solvent polar modes on the adiabatic electron transfer reactions by using the formalism of Hynes. Calculations have been carried out for a model system and also for water and acetonitrile. It is found that, in general, the ultrafast modes can greatly enhance the rate of electron transfer, even by more than an order of magnitude, over the rate obtained by using only the slow overdamped modes usually considered. For water, this acceleration of the rate can be attributed to the high-frequency intermolecular vibrational and librational modes. For a weakly adiabatic reaction, the rate is virtually indistinguishable from the rate predicted by the Marcus transition state theory. Another important result is that even in this case of ultrafast underdamped solvation, energy diffusion appears to be efficient so that electron transfer reaction in water is controlled essentially by the barrier crossing dynamics. This is because the reactant well frequency is-directly proportional to the rate of the initial Gaussian decay of the solvation time correlation function. As a result, the value of the friction at the reactant well frequency rarely falls below the value required for the Kramers turnover except when the polarizability of the water molecules may be neglected. On the other hand, in acetonitrile, the rate of electron transfer reaction is found to be controlled by the energy diffusion dynamics, although a significant contribution to the rate comes also from the barrier crossing rate. Therefore, the present study calls for a need to understand the relaxation of the high-frequency modes in dipolar liquids.

Mechanism of gallic acid biosynthesis in bacteria (Escherichia coli) and walnut (Juglans regia)

Gallic acid (GA), a key intermediate in the synthesis of plant hydrolysable tannins, is also a primary anti-inflammatory, cardio-protective agent found in wine, tea, and cocoa. In this publication, we reveal the identity of a gene and encoded protein essential for GA synthesis. Although it has long been recognized that plants, bacteria, and fungi synthesize and accumulate GA, the pathway leading to its synthesis was largely unknown. Here we provide evidence that shikimate dehydrogenase (SDH), a shikimate pathway enzyme essential for aromatic amino acid synthesis, is also required for GA production. Escherichia coli (E. coli) aroE mutants lacking a functional SDH can be complemented with the plant enzyme such that they grew on media lacking aromatic amino acids and produced GA in vitro. Transgenic Nicotiana tabacum lines expressing a Juglans regia SDH exhibited a 500% increase in GA accumulation. The J. regia and E. coli SDH was purified via overexpression in E. coli and used to measure substrate and cofactor kinetics, following reduction of NADP(+) to NADPH. Reversed-phase liquid chromatography coupled to electrospray mass spectrometry (RP-LC/ESI-MS) was used to quantify and validate GA production through dehydrogenation of 3-dehydroshikimate (3-DHS) by purified E. coli and J. regia SDH when shikimic acid (SA) or 3-DHS were used as substrates and NADP(+) as cofactor. Finally, we show that purified E. coli and J. regia SDH produced GA in vitro.

Non-exponentiality in electron transfer kinetics: Static versus dynamic disorder models

Non-exponential electron transfer kinetics in complex systems are often analyzed in terms of a quenched, static disorder model. In this work we present an alternative analysis in terms of a simple dynamic disorder model where the solvent is characterized by highly non-exponential dynamics. We consider both low and high barrier reactions. For the former, the main result is a simple analytical expression for the survival probability of the reactant. In this case, electron transfer, in the long time, is controlled by the solvent polarization relaxation-in agreement with the analyses of Rips and Jortner and of Nadler and Marcus. The short time dynamics is also non-exponential, but for different reasons. The high barrier reactions, on the other hand, show an interesting dynamic dependence on the electronic coupling element, V-el.

Crystallization of SrCO3 on a self-assembled monolayer substrate: an in-situ synchrotron X-ray study

Self-assembled monolayers (SAMs) of alkanethiols on gold surfaces show great promise in controlling the nucleation and growth of inorganic minerals from solution. In doing so, they mimic the role of some biogenic macromolecules in natural biomineralisation processes. Crystallization on SAM surfaces is usually monitored ex-situ; by allowing the process to commence and to evolve for some time, removing the substrate from the mother solution, and then examining it using microscopy, diffraction etc. We present here for the first time, the use of high energy monochromatic synchrotron X-radiation in conjunction with a two dimensional detector to monitor in situ, in a time resolved fashion, the growth of SrCO3 (strontianite) crystals on a SAM substrate.